$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x + 9$ and $ KL = 7x + 5$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x + 9} = {7x + 5}$ Solve for $x$ $ -4x = -4$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({1}) + 9$ $ KL = 7({1}) + 5$ $ JK = 3 + 9$ $ KL = 7 + 5$ $ JK = 12$ $ KL = 12$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {12} + {12}$ $ JL = 24$